Wendell Ressler Professor of Mathematics
Research
My field is analytic number theory. I study automorphic forms (and automorphic integrals), Dirichlet series, and Hecke correspondence. I am especially interested in Hecke groups, rational period functions, binary quadratic forms and continued fractions.
Publications
W. Ressler, Conjugacy classes and rational period functions for the Hecke groups, Int. J. Number Theory 19 (2023), 757–784. https://dx.doi.org/10.1142/S1793042123500380 [my pdf]
W. Ressler, Hecke symmetry and rational period functions, Ramanujan J. 41 (2016), 323–334. https://doi.org/10.1007/s11139-014-9653-9 [my pdf]
G. Hoang and W. Ressler, Conjugacy classes and binary quadratic forms for the Hecke groups, Canad. Math. Bull. 56 (2013), pp. 570–583. https://dx.doi.org/10.4153/CMB-2012-020-x. [our pdf]
W. Ressler, A Hecke correspondence theorem for automorphic integrals with symmetric rational period
functions on the Hecke groups, J. Number Theory 130 (2010), pp. 2732–2744. https://doi.org/10.1016/j.jnt.2010.06.009 [my pdf]
W. Ressler, On binary quadratic forms and the Hecke groups, Int. J. Number Theory 5 (2009), pp. 1401-1418. https://doi.org/10.1142/S1793042109002730 [my pdf]
W. Culp-Ressler, Rational period functions on the Hecke groups, Ramanujan J. 5 (2001), pp. 281-294. https://doi.org/10.1023/A:1012926712079 [my pdf]
W. Culp-Ressler and W. Pribitkin, A note on Siegel's proof of Hamburger's Theorem, Contemp. Math. 251 (2000), pp.135-140. https://dx.doi.org/10.1090/conm/251 [our pdf]
W. Culp-Ressler, K. Flood, Sr. A. Heath, and W. Pribitkin, On solutions to Riemann's functional equation, Ramanujan J. 4 (2000), pp. 5-9. https://doi.org/10.1023/A:1009836519389 [our pdf]
W. Culp-Ressler, A Hecke correspondence theorem for modular integrals with rational period functions, Illinois J. Math. 40 (1996), pp. 586-605. https://projecteuclid.org/euclid.ijm/1255985938 [my pdf]
Selected Talks
“Conjugacy classes and rational period functions for the Hecke groups," Mid-Atlantic
Seminar On Numbers V, March 27, 2021. [slides]
“The second relation for rational period functions and remainder terms in Hecke correspondence,”
Bryn Mawr Summer Seminar, July 1, 2015. [notes]
“Conjugacy classes for the Hecke groups and related binary quadratic forms,” 29th
Automorphic Forms Workshop, University of Michigan, Ann Arbor, March 3, 2015. [slides]
“Cycle integrals and rational period functions I, II,” Bryn Mawr Summer Seminar, July
24 and August 7, 2014.
“A Perfect Mystery,” Quest For Learning, April 4, 2013.
“Conjugacy classes and binary quadratic forms for the Hecke groups, II,” Bryn Mawr
Summer Seminar, July 12, 2012.
“Conjugacy classes and binary quadratic forms for the Hecke groups,” Bryn Mawr Summer
Seminar, June 28, 2012.
“Conjugacy classes and binary quadratic forms for the Hecke groups,” Joint Mathematics
Colloquium, Franklin & Marshall College and Millersville University, September 28,
2011.
“A Hecke Correspondence Theorem for Automorphic Integrals with Symmetric Rational
Period Functions on the Hecke Groups,” Joint Mathematics Meetings, Washington DC,
January 7, 2009.
Sample of Courses Taught
Fall 2023
Math 109 Calculus I
Math 471 Analytic Number Theory
Spring 2023
Math 331 Introduction to Analysis (2 sections)
Previous semesters
Math 109 Calculus I (2 sections)
Math 471 Topics in Analytic Number Theory
Math 109 Calculus I
Math 110 Calculus II
Math 111 Calculus III
Math 211 Introduction to Higher Mathematics
Math 229 Linear Algebra and Differential Equations
Math 325 Number Theory
Math 329 Fourier Series
Math 331 Introduction to Analysis
Math 442 Complex Analysis
Math 471 Topics in Analytic Number Theory
Publications
W. Ressler, Conjugacy classes and rational period functions for the Hecke groups, Int. J. Number Theory 19 (2023), 757–784. https://dx.doi.org/10.1142/S1793042123500380 [my pdf]
W. Ressler, Hecke symmetry and rational period functions, Ramanujan J. 41 (2016), 323–334. https://doi.org/10.1007/s11139-014-9653-9 [my pdf]
G. Hoang and W. Ressler, Conjugacy classes and binary quadratic forms for the Hecke groups, Canad. Math. Bull. 56 (2013), pp. 570–583. https://dx.doi.org/10.4153/CMB-2012-020-x. [our pdf]
W. Ressler, A Hecke correspondence theorem for automorphic integrals with symmetric rational period functions on the Hecke groups, J. Number Theory 130 (2010), pp. 2732–2744. https://doi.org/10.1016/j.jnt.2010.06.009 [my pdf]
W. Ressler, On binary quadratic forms and the Hecke groups, Int. J. Number Theory 5 (2009), pp. 1401-1418. https://doi.org/10.1142/S1793042109002730 [my pdf]
W. Culp-Ressler, Rational period functions on the Hecke groups, Ramanujan J. 5 (2001), pp. 281-294. https://doi.org/10.1023/A:1012926712079 [my pdf]
W. Culp-Ressler and W. Pribitkin, A note on Siegel's proof of Hamburger's Theorem, Contemp. Math. 251 (2000), pp.135-140. https://dx.doi.org/10.1090/conm/251 [our pdf]
W. Culp-Ressler, K. Flood, Sr. A. Heath, and W. Pribitkin, On solutions to Riemann's functional equation, Ramanujan J. 4 (2000), pp. 5-9. https://doi.org/10.1023/A:1009836519389 [our pdf]
W. Culp-Ressler, A Hecke correspondence theorem for modular integrals with rational period functions, Illinois J. Math. 40 (1996), pp. 586-605. https://projecteuclid.org/euclid.ijm/1255985938 [my pdf]
Selected Talks
“Conjugacy classes and rational period functions for the Hecke groups," Mid-Atlantic Seminar On Numbers V, March 27, 2021. [slides]
“The second relation for rational period functions and remainder terms in Hecke correspondence,” Bryn Mawr Summer Seminar, July 1, 2015. [notes]
“Conjugacy classes for the Hecke groups and related binary quadratic forms,” 29th Automorphic Forms Workshop, University of Michigan, Ann Arbor, March 3, 2015. [slides]
“Cycle integrals and rational period functions I, II,” Bryn Mawr Summer Seminar, July 24 and August 7, 2014.
“A Perfect Mystery,” Quest For Learning, April 4, 2013.
“Conjugacy classes and binary quadratic forms for the Hecke groups, II,” Bryn Mawr Summer Seminar, July 12, 2012.
“Conjugacy classes and binary quadratic forms for the Hecke groups,” Bryn Mawr Summer Seminar, June 28, 2012.
“Conjugacy classes and binary quadratic forms for the Hecke groups,” Joint Mathematics Colloquium, Franklin & Marshall College and Millersville University, September 28, 2011.
“A Hecke Correspondence Theorem for Automorphic Integrals with Symmetric Rational Period Functions on the Hecke Groups,” Joint Mathematics Meetings, Washington DC, January 7, 2009.
Sample of Courses Taught
Fall 2023
Math 109 Calculus I
Math 471 Analytic Number Theory
Spring 2023
Math 331 Introduction to Analysis (2 sections)
Previous semesters
Math 109 Calculus I (2 sections)
Math 471 Topics in Analytic Number Theory
Math 109 Calculus I
Math 110 Calculus II
Math 111 Calculus III
Math 211 Introduction to Higher Mathematics
Math 229 Linear Algebra and Differential Equations
Math 325 Number Theory
Math 329 Fourier Series
Math 331 Introduction to Analysis
Math 442 Complex Analysis
Math 471 Topics in Analytic Number Theory